Multivariate risks and depth-trimmed regions

DOI10.1007/s00780-007-0043-7zbMath1164.91027arXivmath/0606520OpenAlexW2099318798MaRDI QIDQ1003339

Ilya S. Molchanov, Ignacio Cascos

Publication date: 28 February 2009

Published in: Finance and Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606520

zbMATH Keywords

risk measuresValue-at-Riskmultivariate riskdepth-trimmed regionpartially ordered cone

Mathematics Subject Classification ID

Related Items (34)

A duality theory for set-valued functions. I: Fenchel conjugation theory ⋮ Cash subadditive risk measures for portfolio vectors ⋮ SET-VALUED CASH SUB-ADDITIVE RISK MEASURES ⋮ Exact computation of the halfspace depth ⋮ Choosing among notions of multivariate depth statistics ⋮ Intragroup transfers, intragroup diversification and their risk assessment ⋮ Cone distribution functions and quantiles for multivariate random variables ⋮ Multivariate coherent risk measures induced by multivariate convex risk measures ⋮ Depth and outliers for samples of sets and random sets distributions ⋮ Depth level set estimation and associated risk measures ⋮ A directional multivariate value at risk ⋮ Set-valued risk measures for conical market models ⋮ Exact computation of bivariate projection depth and the Stahel-Donoho estimator ⋮ Weighted-mean trimming of multivariate data ⋮ Unnamed Item ⋮ Generalized and robustified empirical depths for multivariate data ⋮ Coherent and convex risk measures for portfolios with applications ⋮ A general solution for robust linear programs with distortion risk constraints ⋮ Nonparametric Imputation by Data Depth ⋮ Multivariate extensions of expectiles risk measures ⋮ Computing zonoid trimmed regions of dimension \(d>2\) ⋮ Risk measures with comonotonic subadditivity or convexity on product spaces ⋮ The expected convex hull trimmed regions of a sample ⋮ Vector risk functions ⋮ Nonlinear expectations of random sets ⋮ Risk arbitrage and hedging to acceptability under transaction costs ⋮ Expectile depth: theory and computation for bivariate datasets ⋮ On general notions of depth for regression ⋮ Consistency of the \(\alpha \)-trimming of a probability. Applications to central regions ⋮ A Comparison of Techniques for Dynamic Multivariate Risk Measures ⋮ On multivariate extensions of conditional-tail-expectation ⋮ Fast Computation of Tukey Trimmed Regions and Median in Dimension p > 2 ⋮ Scalar representation and conjugation of set-valued functions ⋮ MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS

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